Articles publicats en revistes (Matemàtiques i Informàtica)

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Multi-Objective Reinforcement Learning for Designing Ethical Multi-Agent Environments
(Springer Verlag, 2023-08-23) Rodríguez Soto, Manel; López Sánchez, Maite; Rodríguez-Aguilar, Juan A. (Juan Antonio)
This paper tackles the open problem of value alignment in multi-agent systems. In particular, we propose an approach to build an ethical environment that guarantees that agents in the system learn a joint ethically-aligned behaviour while pursuing their respective individual objectives. Our contributions are founded in the framework of Multi-Objective Multi-Agent Reinforcement Learning. Firstly, we characterise a family of Multi-Objective Markov Games (MOMGs), the socalled ethical MOMGs, for which we can formally guarantee the learning of ethical behaviours. Secondly, based on our characterisation we specify the process for building single-objective ethical environments that simplify the learning in the multi-agent system. We illustrate our process with an ethical variation of the Gathering Game, where agents manage to compensate social inequalities by learning to behave in alignment with the moral value of beneficence.
Acyclic reorientation lattices and their lattice quotients
(Springer Verlag, 2024) Pilaud, Vincent
We prove that the acyclic reorientation poset of a directed acyclic graph D is a lattice if and only if the transitive reduction of any induced subgraph of D is a forest. We then show that the acyclic reorientation lattice is always congruence normal, semidistributive (thus congruence uniform) if and only if D is filled, and distributive if and only if D is a forest. When the acyclic reorientation lattice is semidis- tributive, we introduce the ropes of D that encode the join irreducible acyclic reorientations and exploit this combinatorial model in three direc- tions. First, we describe the canonical join and meet representations of acyclic reorientations in terms of non-crossing rope diagrams. Second, we describe the congruences of the acyclic reorientation lattice in terms of lower ideals of a natural subrope order. Third, we use Minkowski sums of shard polytopes of ropes to construct a quotientope for any congruence of the acyclic reorientation lattice.
L-invariants for cohomological representations of PGL(2) over arbitrary number fields
(2024-05-30) Gehrmann, Lennart; Pati, Maria Rosaria
Let π be a cuspidal, cohomological automorphic representation of an inner form G of PGL2 over a number field F of arbitrary signature. Further, let p be a prime of F such that G is split at p and the local component πp of π at p is the Steinberg representation. Assuming that the representation is noncritical at p, we construct automorphic L-invariants for the representation π. If the number field F is totally real, we show that these automorphic L-invariants agree with the Fontaine–Mazur L-invariant of the associated p-adic Galois representation. This generalizes a recent result of Spieß respectively Rosso and the first named author from the case of parallel weight 2 to arbitrary cohomological weights.
A monotonicity theorem for subharmonic functions on manifolds
(Elsevier B.V., 2025-07-07) Kulikov, Aleksei; Nicola, Fabio; Ortega Cerdà, Joaquim; Tilli, Paolo
We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we deduce contractivity estimates for analytic functions on the Riemann sphere, the complex plane and the Poincaré disc, with a complete description of the extremal functions, hence providing a unified and illuminating perspective of a number of results and conjectures on this subject, in particular on the Wehrl entropy conjecture by Lieb and Solovej. In this connection, we completely prove that conjecture for $SU$(2), by showing that the corresponding extremals are only the coherent states. Also, we show that the above (global) estimates admit a local counterpart and in all cases we characterize also the extremal subsets, among those of fixed assigned measure.
Boundary dynamics in unbounded Fatou components.
(American Mathematical Society (AMS), 2025-02-11) Jové Campabadal, Anna; Fagella Rabionet, Núria
We study the behaviour of a transcendental entire map $f: \mathbb{C} \rightarrow \mathbb{C}$ on an unbounded invariant Fatou component $U$, assuming that infinity is accessible from $U$. It is wellknown that $U$ is simply connected. Hence, by means of a Riemann map $\varphi: \mathbb{D} \rightarrow U$ and the associated inner function $g:=\varphi^{-1} \circ f \circ \varphi$, the boundary of $U$ is described topologically in terms of the disjoint union of clusters sets, each of them consisting of one or two connected components in $\mathbb{C}$, improving the results in [BD99; Bar08]. Moreover, under mild assumptions on the location of singular values in $U$ (allowing them even to accumulate at infinity, as long as they accumulate through accesses to $\infty)$, we show that periodic and escaping boundary points are dense in $\partial U$, and that all periodic boundary points accessible from $U$. Finally, under similar conditions, the set of singularities of $g$ is shown to have zero Lebesgue measure, strengthening substantially the results in [EFJS19; ERS20].
Dynamics of projectable functions: Towards an atlas of wandering domains for a family of Newton maps.
(Cambridge University Press (CUP), 2024-11-25) Florido Llinàs, Robert; Fagella Rabionet, Núria
We present a one-parameter family $F_\lambda$ of transcendental entire functions with zeros, whose Newton's method yields wandering domains, coexisting with the basins of the roots of $F_\lambda$. Wandering domains for Newton maps of zero-free functions have been built before by, e.g. Buff and Rückert [23] based on the lifting method. This procedure is suited to our Newton maps as members of the class of projectable functions (or maps of the cylinder), i.e. transcendental meromorphic functions $f(z)$ in the complex plane that are semiconjugate, via the exponential, to some map $g(w)$, which may have at most a countable number of essential singularities. In this paper, we make a systematic study of the general relation (dynamical and otherwise) between $f$ and $g$, and inspect the extension of the logarithmic lifting method of periodic Fatou components to our context, especially for those $g$ of finite-type. We apply these results to characterize the entire functions with zeros whose Newton's method projects to some map $g$ which is defined at both 0 and $\infty$. The family $F_\lambda$ is the simplest in this class, and its parameter space shows open sets of $\lambda$-values in which the Newton map exhibits wandering or Baker domains, in both cases regions of initial conditions where Newton's root-finding method fails.
LungHist700: A dataset of histological images for deep learning in pulmonary pathology
(Springer Nature, 2024-10-05) Diosdado, Jorge; Gilabert Roca, Pere; Seguí Mesquida, Santi; Borrego, Henar
Accurate detection and classification of lung malignancies are crucial for early diagnosis, treatment planning, and patient prognosis. Conventional histopathological analysis is time-consuming, limiting its clinical applicability. To address this, we present a dataset of 691 high-resolution (1200 × 1600 pixels) histopathological lung images, covering adenocarcinomas, squamous cell carcinomas, and normal tissues from 45 patients. These images are subdivided into three differentiation levels for both pathological types: well, moderately, and poorly differentiated, resulting in seven classes for classification. The dataset includes images at 20x and 40x magnification, reflecting real clinical diversity. We evaluated image classification using deep neural network and multiple instance learning approaches. Each method was used to classify images at 20x and 40x magnification into three superclasses. We achieved accuracies between 81% and 92%, depending on the method and resolution, demonstrating the dataset’s utility.
Inhomogeneous Poisson processes in the disk and interpolation
(Cambridge University Press (CUP), 2024-04-30) Hartmann, Andreas; Massaneda Clares, Francesc Xavier
We investigate different geometrical properties, related to Carleson measures and pseudo-hyperbolic separation, of inhomogeneous Poisson point processes on the unit disk. In particular, we give conditions so that these random sequences are almost surely interpolating for the Hardy, Bloch or weighted Dirichlet spaces.
Cyclic coverings of genus 2 curves of Sophie Germain type
(2024-05-21) Naranjo del Val, Juan Carlos; Ortega Ortega, Angela; Spelta, Irene
We consider cyclic unramified coverings of degree $d$ of irreducible complex smooth genus 2 curves and their corresponding Prym varieties. They provide natural examples of polarized abelian varieties with automorphisms of order $d$. The rich geometry of the associated Prym map has been studied in several papers, and the cases $d=2,3,5,7$ are quite well understood. Nevertheless, very little is known for higher values of $d$. In this paper, we investigate whether the covering can be reconstructed from its Prym variety, that is, whether the generic Prym Torelli theorem holds for these coverings. We prove this is so for the so-called Sophie Germain prime numbers, that is, for $d \geq 11$ prime such that $\frac{d-1}{2}$ is also prime. We use results of arithmetic nature on $G L_2$-type abelian varieties combined with theta-duality techniques.
How to determine a curve singularity
(Canadian Mathematical Society., 2024-01-09) Elías García, Joan
We characterize the finite codimension sub-k-algebras of $\mathbf{k} \llbracket t \rrbracket$ as the solutions of a computable finite family of higher differential operators. For this end, we establish a duality between such a sub-algebras and the finite codimension $\mathbf{k}$-vector spaces of $\mathbf{k}[u]$, this ring acts on $\mathbf{k} \llbracket t \rrbracket$ by differentiation.
Overcoming Diverse Undesired Effects in Recommender Systems: A Deontological Approach
(Association for Computing Machinery, 2024-07-27) Gómez Duran, Paula; Gilabert Roca, Pere; Seguí Mesquida, Santi; Vitrià i Marca, Jordi
In today’s digital landscape, recommender systems have gained ubiquity as a means of directing users towards personalized products, services, and content. However, despite their widespread adoption and a long track of research, these systems are not immune to shortcomings. A significant challenge faced by recommender systems is the presence of biases, which produces various undesirable effects, prominently the popularity bias. This bias hampers the diversity of recommended items, thus restricting users’ exposure to less popular or niche content. Furthermore, this issue is compounded when multiple stakeholders are considered, requiring the balance of multiple, potentially conflicting objectives. In this paper, we present a new approach to address a wide range of undesired consequences in recommender systems that involve various stakeholders. Instead of adopting a consequentialist perspective that aims to mitigate the repercussions of a recommendation policy, we propose a deontological approach centered around a minimal set of ethical principles. More precisely, we introduce two distinct principles aimed at avoiding overconfidence in predictions and accurately modeling the genuine interests of users. The proposed approach circumvents the need for defining a multi-objective system, which has been identified as one of the main limitations when developing complex recommenders. Through extensive experimentation, we show the efficacy of our approach in mitigating the adverse impact of the recommender from both user and item perspectives, ultimately enhancing various beyond accuracy metrics. This study underscores the significance of responsible and equitable recommendations and proposes a strategy that can be easily deployed in real-world scenarios.
Analysing Conversation Pathways with a Chatbot Tutor to Enhance Self-Regulation in Higher Education
(MDPI, 2024-05-30) Martins Gironelli, Ludmila; Fernández Ferrer, Maite; Puertas i Prats, Eloi
Chatbots can have a significant positive impact on learning. There is a growing interest in their application in teaching and learning. The self-regulation of learning is fundamental for the development of lifelong learning skills, and for this reason, education should contribute to its development. In this sense, the potential of chatbot technologies for supporting students to self-regulate their learning activity has already been pointed out. The objective of this work is to explore university students’ interactions with EDUguia chatbot to understand whether there are patterns of use linked to phases of self-regulated learning and academic task completion. This study presents an analysis of conversation pathways with a chatbot tutor to enhance self-regulation skills in higher education. Some relevant findings on the length, duration, and endpoints of the conversations are shared. In addition, patterns in these pathways and users’ interactions with the tool are analysed. Some findings are relevant to the analysis of the link between design and user experience, but they can also be related to implementation decisions. The findings presented could contribute to the work of other educators, designers, and developers interested in developing a tool addressing this goal.
Chasing spammers: Using the Internet protocol address fordetection
(John Wiley & Sons, 2024-06-01) Sáez Ortuño, Laura; Forgas Coll, Santiago; Huertas García, Rubén; Puertas i Prats, Eloi
The proliferation of reviews evaluating different services on social networks andonline platforms and their importance in consumer decision‐making has led someunscrupulous individuals to take advantage of the anonymity offered by the Internetto manipulate these reviews and influence customers' decisions. The main objectivesof this study are: (1) to test whether spammers usually perform their misdemeanorsfrom the same IP address; (2) to explore whether there are differences betweenstated sexes in this regard; (3) to detect the main motivations for posting fraudulentreviews; and (4) to determine the motivations for doing so from the same IP address.These objectives were achieved by means of a quasi‐experiment with a sample of7,192,487 users, and a qualitative investigation in which 37 users who had falsifiedinformation were interviewed. The results show that spammers who tend to faketheir identity do so from the same IP address and that they tend to be male. Fourtypes of motivation are presented: revenge, entertainment, opportunity for profit,and self‐esteem; as well as a further three to explain the use of the same IP:convenience, limited resources, and complacency.
Higher differentiability results for solutions to a class of non-homogeneous elliptic problems under sub-quadratic growth conditions
(World Scientific Publishing, 2023-05-29) Clop, Albert; Gentile, Andrea; Passarelli di Napoli, Antonia
We prove a sharp higher differentiability result for local minimizers of functionals of the form $$ \mathscr{F}(w, \Omega)=\int_{\Omega}[F(x, D w(x))-f(x) \cdot w(x)] d x $$ with non-autonomous integrand $F(x, \xi)$ which is convex with respect to the gradient variable, under $p$-growth conditions, with $1
Nonlinear transport equations and quasiconformal maps
(Finnish Mathematical Society, 2023-05-16) Clop, Albert; Sengupta, Banhirup
We prove existence of solutions to a nonlinear transport equation in the plane,for which the velocity field is obtained as the convolution ofthe classical Cauchy kernel with theunknown. Even though the initial datum is bounded and compactly supported, the velocity fieldmay have unbounded divergence. The proof is based on the compactness property of quasiconformalmappings
Medigan: A Python library of pretrained generative models for medical image synthesis
(Society of Photo-Optical Instrumentation Engineers (SPIE), 2023-02-20) Osuala, Richard; Skorupko, Grzegorz; Lazrak, Noussair; Garrucho, Lidia; García, Eloy; Joshi, Smriti; Jouide El Kaderi, Socayna; Rutherford, Michael; Prior, Fred; Kushibar, Kaisar; Díaz, Oliver; Lekadir, Karim, 1977-
Purpose: Deep learning has shown great promise as the backbone of clinical decision support systems. Synthetic data generated by generative models can enhance the performance and capabilities of data-hungry deep learning models. However, there is (1) limited availability of (synthetic) datasets and (2) generative models are complex to train, which hinders their adoption in research and clinical applications. To reduce this entry barrier, we explore generative model sharing to allow more researchers to access, generate, and benefit from synthetic data. Approach: We propose medigan, a one-stop shop for pretrained generative models imple- mented as an open-source framework-agnostic Python library. After gathering end-user requirements, design decisions based on usability, technical feasibility, and scalability are formulated. Subsequently, we implement medigan based on modular components for generative model (i) execution, (ii) visualization, (iii) search & ranking, and (iv) contribution. We integrate pre- trained models with applications across modalities such as mammography, endoscopy, x-ray, and MRI. Results: The scalability and design of the library are demonstrated by its growing number of integrated and readily-usable pretrained generative models, which include 21 models utilizing nine different generative adversarial network architectures trained on 11 different datasets. We further analyze three medigan applications, which include (a) enabling community-wide sharing of restricted data, (b) investigating generative model evaluation metrics, and (c) improving clinical downstream tasks. In (b), we extract Fréchet inception distances (FID) demonstrating FID variability based on image normalization and radiology-specific feature extractors. Conclusion: medigan allows researchers and developers to create, increase, and domain-adapt their training data in just a few lines of code. Capable of enriching and accelerating the development of clinical machine learning models, we show medigan’s viability as platform for generative model sharing. Our multimodel synthetic data experiments uncover standards for assessing and reporting metrics, such as FID, in image synthesis studies.
A large-scale multicenter breast cancer DCE-MRI benchmark dataset with expert segmentations
(Springer Nature, 2025-03-19) Garrucho, Lidia; Kushibar, Kaisar; Reidel, Claire-Anne; Joshi, Smriti; Osuala, Richard; Tsirikoglou, Apostolia; Bobowicz, Maciej; Riego, Javier del; Catanese, Alesandro; Gwoździewicz, Katarzyna; Cosaka, Maria Laura; Abo-Elhoda, Pasant M.; Tantawy, Sara W.; Sakrana, Shorouq S.; Shawky-Abdelfatah, Norhan O.; Abdo-Salem, Amr Muhammad; Kozana, Androniki; Divjak, Eugen; Ivanac, Gordana; Nikiforaki, Katerina; Klontzas, Michail E.; García Dosdá, Rosa; Gulsun-Akpinar, Meltem; Lafcı, Oğuz; Mann, Ritse; Martín-Isla, Carlos; Prior, Fred; Marias, Kostas; Starmans, Martijn P. A.; Strand, Fredrik; Díaz, Oliver; Igual Muñoz, Laura; Lekadir, Karim, 1977-
Artificial Intelligence (AI) research in breast cancer Magnetic Resonance Imaging (MRI) faces challenges due to limited expert-labeled segmentations. To address this, we present a multicenter dataset of 1506 pre-treatment T1-weighted dynamic contrast-enhanced MRI cases, including expert annotations of primary tumors and non-mass-enhanced regions. The dataset integrates imaging data from four collections in The Cancer Imaging Archive (TCIA), where only 163 cases with expert segmentations were initially available. To facilitate the annotation process, a deep learning model was trained to produce preliminary segmentations for the remaining cases. These were subsequently corrected and verified by 16 breast cancer experts (averaging 9 years of experience), creating a fully annotated dataset. Additionally, the dataset includes 49 harmonized clinical and demographic variables, as well as pre-trained weights for a baseline nnU-Net model trained on the annotated data. This resource addresses a critical gap in publicly available breast cancer datasets, enabling the development, validation, and benchmarking of advanced deep learning models, thus driving progress in breast cancer diagnostics, treatment response prediction, and personalized care.
High-resolution synthesis of high-density breast mammograms: Application to improved fairness in deep learning based mass detection
(Frontiers Media, 2023-01-23) Garrucho, Lidia; Kushibar, Kaisar; Osuala, Richard; Díaz, Oliver; Catanese, Alesandro; Riego, Javier del; Bobowicz, Maciej; Strand, Fredrik; Igual Muñoz, Laura; Lekadir, Karim, 1977-
Computer-aided detection systems based on deep learning have shown goodperformance in breast cancer detection. However, high-density breasts showpoorer detection performance since dense tissues can mask or even simulatemasses. Therefore, the sensitivity of mammography for breast cancer detectioncan be reduced by more than 20% in dense breasts. Additionally, extremelydense cases reported an increased risk of cancer compared to low-densitybreasts. This study aims to improve the mass detection performance in highdensitybreasts using synthetic high-density full-field digital mammograms(FFDM) as data augmentation during breast mass detection model training. Tothis end, a total of five cycle-consistent GAN (CycleGAN) models using threeFFDM datasets were trained for low-to-high-density image translation in highresolutionmammograms. The training images were split by breast density BIRADScategories, being BI-RADS A almost entirely fatty and BI-RADS Dextremely dense breasts. Our results showed that the proposed dataaugmentation technique improved the sensitivity and precision of massdetection in models trained with small datasets and improved the domaingeneralization of the models trained with large databases. In addition, theclinical realism of the synthetic images was evaluated in a reader studyinvolving two expert radiologists and one surgical oncologist.
Machine and deep learning for longitudinal biomedical data: a review of methods and applications
(Springer Verlag, 2023-11) Cascarano, Anna; Mur Petit, Jordi; Hernández-González, Jerónimo; Camacho, Marina; Toro Eadie, Nina de; Gkontra, Polyxeni; Chadeau-Hyam, Marc; Vitrià i Marca, Jordi; Lekadir, Karim, 1977-
Exploiting existing longitudinal data cohorts can bring enormous benefits to the medical field, as many diseases have a complex and multi-factorial time-course, and start to develop long before symptoms appear. With the increasing healthcare digitisation, the application of machine learning techniques for longitudinal biomedical data may enable the development of new tools for assisting clinicians in their day-to-day medical practice, such as for early diagnosis, risk prediction, treatment planning and prognosis estimation. However, due to the heterogeneity and complexity of time-varying data sets, the development of suitable machine learning models introduces major challenges for data scientists as well as for clinical researchers. This paper provides a comprehensive and critical review of recent developments and applications in machine learning for longitudinal biomedical data. Although the paper provides a discussion of clustering methods, its primary focus is on the prediction of static outcomes, defined as the value of the event of interest at a given instant in time, using longitudinal features, which has emerged as the most commonly employed approach in healthcare applications. First, the main approaches and algorithms for building longitudinal machine learning models are presented in detail, including their technical implementations, strengths and limitations. Subsequently, most recent biomedical and clinical applications are reviewed and discussed, showing promising results in a wide range of medical specialties. Lastly, we discuss current challenges and consider future directions in the field to enhance the development of machine learning tools from longitudinal biomedical data.
Ein–Lazarsfeld–Mustopa conjecture for the blow-up of a projective space
(Springer Verlag, 2023-01-18) Miró-Roig, Rosa M. (Rosa Maria); Salat Moltó, Martí
We solve the Ein-Lazarsfeld-Mustopa conjecture for the blow up of a projective space along a linear subspace. More precisely, let $X$ be the blow up of $\mathbb{P}^n$ at a linear subspace and let $L$ be any ample line bundle on $X$. We show that the syzygy bundle $M_L$ defined as the kernel of the evalution map $H^0(X, L) \otimes \mathcal{O}_X \rightarrow L$ is $L$-stable. In the last part of this note we focus on the rigidness of $M_L$ to study the local shape of the moduli space around the point $\left[M_L\right]$.

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